Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Westdickenberg, Maria G."'
We capture optimal decay for the Mullins-Sekerka evolution, a nonlocal, parabolic free boundary problem from materials science. Our main result establishes convergence of BV solutions to the planar profile in the physically relevant case of ambient s
Externí odkaz:
http://arxiv.org/abs/2309.14215
In this paper we derive optimal relaxation rates for the Cahn-Hilliard equation on the one-dimensional torus and the line. We consider initial conditions with a finite (but not small) $L^1$-distance to an appropriately defined bump. The result extend
Externí odkaz:
http://arxiv.org/abs/2104.14004
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, R
Externí odkaz:
http://arxiv.org/abs/2104.03689
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We establish sufficient conditions for a function on the torus to be equal to its Steiner symmetrization and apply the result to volume-constrained minimizers of the Cahn-Hilliard energy. We also show how two-point rearrangements can be used to estab
Externí odkaz:
http://arxiv.org/abs/1907.08112
In this paper we derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance---in terms of either a first moment or the excess mass---to a kink profi
Externí odkaz:
http://arxiv.org/abs/1806.02519
We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in the conte
Externí odkaz:
http://arxiv.org/abs/1709.04833
We establish metastability of the one-dimensional Cahn-Hilliard equation for initial data that is order-one in energy and order-one in $\dot{H}^{-1}$ away from a point on the so-called slow manifold with $N$ well-separated layers. Specifically, we sh
Externí odkaz:
http://arxiv.org/abs/1705.10985
The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to $-1$. Existence and properties of a "droplet-shaped" local energy minimizer are established. A standard mountain pass argu
Externí odkaz:
http://arxiv.org/abs/1510.00061
We study the d-dimensional Cahn-Hilliard equation on the flat torus in a parameter regime in which the system size is large and the mean value is close---but not too close---to -1. We are particularly interested in a quantitative description of the e
Externí odkaz:
http://arxiv.org/abs/1404.5913